An Introduction to Logic - Second Edition: Using Natural Deduction, Real Arguments, a Little History, and Some Humour

In lively and readable prose, Arthur presents a new approach to the study of logic, one that seeks to integrate methods of argument analysis developed in modern “informal logic” with natural deduction techniques. The dry bones of logic are given flesh by unusual attention to the history of the subject, from Pythagoras, the Stoics, and Indian Buddhist logic, through Lewis Carroll, Venn, and Boole, to Russell, Frege, and Monty Python. A previous edition of this book appeared under the title Natural Deduction. This new edition adds clarifications of the notions of explanation, validity and formal validity, a more detailed discussion of derivation strategies, and another rule of inference, Reiteration.

Table of Contents:
Preface for Students Preface for Instructors Acknowledgements PART I: ARGUMENTS Chapter 1: Arguments Introduction Identifying Arguments Inference Indicators Explanations Implicit Arguments Enthymemes Natural Arguments Argument and Inference Techniques of Diagramming Chapter 2: Validity Validity Defining Validity Soundness Argument Forms and Formal Validity Evaluating Natural Arguments PART II: STATEMENT LOGIC Chapter 3: Statements and Conditionals Statements and Compounds Statements Compounds Statement Operators Conditional Statements Modus Ponens Argument Form and Substitution Instance Affirming the Consequent Chapter 4: Negation Symbolizing Negations Negations Contradictories Modus Tollens Modus Tollens and Double Negation Denying the Antecedent Inference and Implication Chapter 5: Conjunction Symbolizing Conjunctions Rules of Inference for Conjunction Evaluating Extended Arguments Chapter 6: Disjunction Symbolizing Disjunctions Rules of Inference for Disjunctions Disjunctive Syllogism Disjunction De Morgan’s Laws Chapter 7: Conditional Proof More on Symbolizing Disjunctions in Conditionals ‘Unless’ ‘Otherwise,’ ‘Else’ More Rules Involving Conditionals Conditional Proof and Supposition The Hypothetical Syllogism Supposition in Natural Argument Chapter 8: Biconditionals Necessary and Sufficient Conditions ‘Only If’ Necessary and Sufficient Conditions Biconditionals Symbolizing Conversational Implicature Rules of Inference Chapter 9: Dilemmas Dilemmas Natural Dilemmas Chapter 10: Reductio Arguments Reductio ad Absurdum Natural Reductio Arguments Chapter 11: Review and Consolidation Rules of Inference Rules of Inference and Equivalence Rules Two Simplifying Modifications Proof Strategies Derived Rules Chapter 12: SL as a Formal System Rules of Formation Symbols, Formulas, and Wffs Consistency and Completeness Sequents, Theorems, and Axioms Sequents and Theorems Axioms and the Propositional Calculus Chapter 13: Truth Tables Truth Tables and Statements Truth Tables Material Implication Tautologies, Contradictions, and Contingent Statements Logical Equivalence Truth Tables and Validity The Full Truth Table Method Invalid Argument Forms The Brief Truth Table Method Chapter 14: Truth Trees for SL Truth Trees The Truth Tree Method Decomposition Rules Statements, Consistency, and Completeness Tautologies, Contradictions, and Logical Equivalence Consistency and Completeness PART III: PREDICATE LOGIC Chapter 15: Syllogistic Logic Category Logic Aristotle’s Logic A-, E-, I-, and O-Statements Ambiguous Statements Carroll Diagrams Carroll’s Diagrams Existence and Non-Existence Conversion Evaluating Validity of Syllogisms Chapter 16: Universal Quantification Universal and Singular Statements Universal Quantification ‘Only’ and ‘Nothing But’ Singular Statements and Individual Names Rules of Inference: UI and UG Chapter 17: Existential Quantification Particular Statements Existential Quantification Rules of Inference Existential Instantiation Existential Generalization Proof Strategy Chapter 18: Advanced Class Logic Arguments with More than 3 Predicates Carroll Diagrams for 4 or 5 Categories Sorites Existential Import On Giving Universal Statements Existential Import Penevalid Arguments Non-Emptiness of the UD Chapter 19: Asyllogistic Arguments More on Symbolizing Non-Classical Statements ‘Any’ Asyllogistic Proofs: QN Predicate Logic as a Formal System Symbols, Formulas, and Wffs Propositional Functions and Quantifier Scope Chapter 20: Relational Logic The Logic of Relations Relations Symbolizing Relations Nested Quantifiers Relational Proofs Properties of Binary Relations Transitivity, Symmetry, and Reflexivity Equivalence Relations Chapter 21: Logic with Identity Identity and Quantity Symbolizing Identities and Quantities Russell’s Theory of Definite Descriptions Inferences Involving Identity The Rule of Inference SI Properties of Identity Ordering Relations Chapter 22: Relational Arguments More on Symbolizing Relational Statements A Method for Symbolizing Prenex Forms Relational Arguments Arguments beyond the Scope of Traditional Logic Ambiguities and the Quantifier Shift Fallacy Chapter 23: Truth Trees for PL Predicate Logic Truth Trees Truth Tree Rules from Statement Logic Additional Truth Tree Rules for Quantifications Negated Quantifier Decomposition Rules Effective Completeness Trees for Relational Logic and Identity Truth Tree Rules in Relational Logic Additional Truth Tree Rules for Identity and Diversity Chapter 24: Other Logics Second Order Logic Modal Logic Deontic Logic Quantum Logic Intuitionistic Logic Appendix 1: The Paradoxes of Material Implication Appendix 2: A Little History: Consequentiae Appendix 3: Logic Diagrams Glossary Index

About the Author :
Richard T.W. Arthur is Professor of Philosophy at McMaster University.

Review :
“Richard Arthur’s book offers a fresh new perspective on the pedagogy of introductory logic instruction and its underlying philosophy. Its approach makes informal logic and critical thinking mesh smoothly and intuitively with formal logic, thus clarifying the relevance of formal logic to the assessment of natural argument. My experience of teaching from the first edition was very positive; the book genuinely makes a majority of students build an appetite for logic. With its many conceptual, technical, and pedagogical improvements, the second edition should prove to be a sound choice as an introductory logic text.” — Nicolas Fillion, Simon Fraser University Praise for the first edition: “This excellent text covers all the standard topics and more. Its real strength lies in the clarity and humour of exposition and in the richness of examples and exercises. The illustrations are invariably interesting, since often they are related to current events or the history of philosophy and science or are drawn from Monty Python. The last of these provides several memorable fallacies. Arthur’s … is one of the finest introductions to logic available today.” — James Robert Brown, University of Toronto